The Nexus 10 was a great tablet and is still perfectly useable for the average consumer. Unfortunately, Google has decided not to update it to Android 6.0 Marshmallow. However, just because Google won’t update it, doesn’t mean you can’t.
Since this is a Nexus device, the updating process is a lot easier than it would be for other tablets. Dmitry Grinberg, the same person who posted instructions on how to install the Marshmallow update on the Nexus 4, has also posted instructions on how to install the Android 6.0 update on the Nexus 10.
If you don’t want or know how to do it yourself, he has also included a pre-built AOSP Marshmallow image that you can download. To see the full instructions, head over to his site.